Journal of Probability and Statistics
Volume 2011 (2011), Article ID 765058, 11 pages
http://dx.doi.org/10.1155/2011/765058
Research Article

Lower Confidence Bounds for the Probabilities of Correct Selection

Radhey S. Singh1 and Narinder Kumar2

1Department of Mathematics and Statistics, University of Guelph, ON, Canada N1G 2W1
2Department of Statistics, Panjab University, Chandigarh 160014, India

Received 6 October 2010; Accepted 12 January 2011

Academic Editor: A. Thavaneswaran

Copyright © 2011 Radhey S. Singh and Narinder Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend the results of Gupta and Liang (1998), derived for location parameters, to obtain lower confidence bounds for the probability of correctly selecting the 𝑡 best populations ( P C S 𝑡 ) simultaneously for all 𝑡 = 1 , … , 𝑘 − 1 for the general scale parameter models, where 𝑘 is the number of populations involved in the selection problem. The application of the results to the exponential and normal probability models is discussed. The implementation of the simultaneous lower confidence bounds for P C S 𝑡 is illustrated through real-life datasets.